Write a class that contains the following two methods:

/** Convert from Celsius to Fahrenheit */
public static double celsiusToFahrenheit(double celsius)

/** Convert from Fahrenheit to Celsius */
public static double fahrenheitToCelsius(double fahrenheit)

The formula for the conversion is:

$$fahrenheit = (9.0 / 5) * celsius + 32$$

$$celsius = (5.0 / 9) * (fahrenheit – 32)$$

Write a test program that invokes these methods to display the following tables:

Celsius     Fahrenheit      |   Fahrenheit      Celsius
40.0        104.0           |   120.0           48.89
39.0        102.2           |   110.0           43.33
...
32.0        89.6            |   40.0            4.44
31.0        87.8            |   30.0            -1.11

(Financial application: compute the future investment value) Write a method that computes future investment value at a given interest rate for a specified number of years. The future investment is determined using the formula in Programming Exercise 2.21.

Use the following method header:

public static double futureInvestmentValue(
double investmentAmount, double monthlyInterestRate,int years)

For example, futureInvestmentValue(10000, 0.05/12, 5) returns 12833.59 .

Write a test program that prompts the user to enter the investment amount (e.g., 1,000) and the interest rate (e.g., 9%) and prints a table that displays future value for the years from 1 to 30, as shown below:

The amount invested: 1000
Annual interest rate: 9
Years      Future Value
1              1093.80
2              1196.41
...
29            13467.25
30            14730.57

Write a method to display a pattern as follows:

              1
            2 1
          3 2 1
...
n n-1 ... 3 2 1

The method header is

public static void displayPattern(int n)

What would be wrong with not writing a return statement in a value-returning method? Can you have a return statement in a void method? Does the return statement in the following method cause syntax errors?

public static void xMethod(double x, double y) {
 System.out.println(x + y);
 return x + y;
}

What is the return type of a main method?

A high school has a 400-m oval track. If Parry runs around the track eight times, how many kilometers has she traveled?

(Display an integer reversed) Write a method with the following header to ­display an integer in reverse order:

public static void reverse(int number)

For example, reverse(3456) displays 6543 . Write a test program that prompts the user to enter an integer then displays its reversal.

True or false? A call to a method with a void return type is always a statement itself, but a call to a value-returning method cannot be a statement by itself.

(Geometry: point position) Programming Exercise 3.32 shows how to test whether a point is on the left side of a directed line, on the right, or on the same line. Write the methods with the following headers:

/** Return true if point (x2, y2) is on the left side of the
* directed line from (x0, y0) to (x1, y1) */
public static boolean leftOfTheLine(double x0, double y0,
double x1, double y1, double x2, double y2)

/** Return true if point (x2, y2) is on the same
* line from (x0, y0) to (x1, y1) */
public static boolean onTheSameLine(double x0, double y0,
double x1, double y1, double x2, double y2)

/** Return true if point (x2, y2) is on the
* line segment from (x0, y0) to (x1, y1) */
public static boolean onTheLineSegment(double x0, double y0,
double x1, double y1, double x2, double y2)

Write a program that prompts the user to enter the three points for p0 , p1 , and p2 and displays whether p2 is on the left side of the line from p0 to p1 , right side, the same line, or on the line segment. Here are some sample runs:

Enter three points for p0, p1, and p2: 1 1 2 2 1.5 1.5
(1.5, 1.5) is on the line segment from (1.0, 1.0) to (2.0, 2.0)

Enter three points for p0, p1, and p2: 1 1 2 2 3 3
(3.0, 3.0) is on the same line from (1.0, 1.0) to (2.0, 2.0)

Enter three points for p0, p1, and p2: 1 1 2 2 1 1.5
(1.0, 1.5) is on the left side of the line
from (1.0, 1.0) to (2.0, 2.0)

Enter three points for p0, p1, and p2: 1 1 2 2 1 –1
(1.0, −1.0) is on the right side of the line
from (1.0, 1.0) to (2.0, 2.0)

Use the methods in the following program to print 100 uppercase letters and then 100 single digits, printing ten per line.

1   public class RandomCharacter {
2       /** Generate a random character between ch1 and ch2 */
3       public static char getRandomCharacter(char ch1, char ch2) {
4           return (char)(ch1 + Math.random() * (ch2 - ch1 + 1));
5       }
6
7       /** Generate a random lowercase letter */
8       public static char getRandomLowerCaseLetter() {
9           return getRandomCharacter('a', 'z');
10      }
11
12      /** Generate a random uppercase letter */
13      public static char getRandomUpperCaseLetter() {
14          return getRandomCharacter('A', 'Z');
15      }
16
17      /** Generate a random digit character */
18      public static char getRandomDigitCharacter() {
19          return getRandomCharacter('0', '9');
20      }
21
22      /** Generate a random character */
23      public static char getRandomCharacter() {
24          return getRandomCharacter('\u0000', '\uFFFF');
25      }
26  }

Write a method with the following header to format the integer with the specified width. public static String format(int number, int width) The method returns a string for the number with one or more prefix 0s. The size of the string is the width. For example, format(34, 4) returns 0034 and format(34, 5) returns 00034. If the number is longer than the width, the method returns the string representation for the number. For example, format(34, 1) returns 34. Write a test program that prompts the user to enter a number and its width and displays a string returned by invoking format(number, width).

A regular polygon is an n-sided polygon in which all sides are of the same length and all angles have the same degree (i.e., the polygon is both equilateral and equiangular). The formula for computing the area of a regular polygon is:

$$\text { Area }=\frac{n \times s^2}{4 \times \tan \left(\frac{\pi}{n}\right)}$$

Write a method that returns the area of a regular polygon using the following header:

public static double area(1nt $\mathrm{n}$, double side)

Write a main method that prompts the user to enter the number of sides and the side of a regular polygon and displays its area.

The area of a pentagon can be computed using the following formula:

$$\text { Area }=\frac{5 \times s^2}{4 \times \tan \left(\frac{\pi}{5}\right)}$$

Write a method that returns the area of a pentagon using the following header:

public static double area(double side)

Write a main method that prompts the user to enter the side of a pentagon and displays its area.

(Print calendar) Programming Exercise 3.21 uses Zeller’s congruence to calculate the day of the week. Simplify Listing 6.12, PrintCalendar.java, using Zeller’s algorithm to get the start day of the month.